We investigate the synchronization transitions in systems of coupled Kuramoto-Sakaguchi phase oscillators. We show that in globally coupled systems with certain unimodal frequency distributions, there can appear unusual types of synchrony transitions, where synchrony can decay with increasing coupling, incoherence can regain stability for increasing coupling, or multistability between partially synchronized states and/or the incoherent state can appear. In one-dimensional arrays of oscillators with non-local coupling one can observe at the onset of synchrony the emergence of collective macroscopic chaos as an intermediate stage between complete incoherence and stable partially coherent plane waves. In both cases, the phase lag in the interaction function plays an important role for the observed phenomena.